{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:AHG3TJA7WVGWC47M2UU2NMGDLS","short_pith_number":"pith:AHG3TJA7","schema_version":"1.0","canonical_sha256":"01cdb9a41fb54d6173ecd529a6b0c35c88c3a701d92ace74f40775f43c52edb6","source":{"kind":"arxiv","id":"2402.18810","version":4},"attestation_state":"computed","paper":{"title":"The numeraire e-variable and reverse information projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Aaditya Ramdas, Johannes Ruf, Martin Larsson","submitted_at":"2024-02-29T02:31:42Z","abstract_excerpt":"We consider testing a composite null hypothesis $\\mathcal{P}$ against a point alternative $\\mathsf{Q}$ using e-variables, which are nonnegative random variables $X$ such that $\\mathbb{E}_\\mathsf{P}[X] \\leq 1$ for every $\\mathsf{P} \\in \\mathcal{P}$. This paper establishes a fundamental result: under no conditions whatsoever on $\\mathcal{P}$ or $\\mathsf{Q}$, there exists a special e-variable $X^*$ that we call the numeraire, which is strictly positive and satisfies $\\mathbb{E}_\\mathsf{Q}[X/X^*] \\leq 1$ for every other e-variable $X$. In particular, $X^*$ is log-optimal in the sense that $\\mathbb"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2402.18810","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-02-29T02:31:42Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"cc4051c5510555b7a133bee100b478cb654fd9541d296538bf8825cbfce3d519","abstract_canon_sha256":"007eb190f180f166f3d9da0299dd71a2be4f17ee34d0454b9e4e5c5d60ff58c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:08:52.481835Z","signature_b64":"pTEURCjuuwRbTJYB3Fi0D4vBbxdXuSYOKazCYQkHPoTiQR4x8W8b6FXJBM3t8Jp/5Z4+e9RLQ5+sbASLkQstCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01cdb9a41fb54d6173ecd529a6b0c35c88c3a701d92ace74f40775f43c52edb6","last_reissued_at":"2026-07-05T10:08:52.481476Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:08:52.481476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The numeraire e-variable and reverse information projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Aaditya Ramdas, Johannes Ruf, Martin Larsson","submitted_at":"2024-02-29T02:31:42Z","abstract_excerpt":"We consider testing a composite null hypothesis $\\mathcal{P}$ against a point alternative $\\mathsf{Q}$ using e-variables, which are nonnegative random variables $X$ such that $\\mathbb{E}_\\mathsf{P}[X] \\leq 1$ for every $\\mathsf{P} \\in \\mathcal{P}$. This paper establishes a fundamental result: under no conditions whatsoever on $\\mathcal{P}$ or $\\mathsf{Q}$, there exists a special e-variable $X^*$ that we call the numeraire, which is strictly positive and satisfies $\\mathbb{E}_\\mathsf{Q}[X/X^*] \\leq 1$ for every other e-variable $X$. In particular, $X^*$ is log-optimal in the sense that $\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.18810","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.18810/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2402.18810","created_at":"2026-07-05T10:08:52.481532+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.18810v4","created_at":"2026-07-05T10:08:52.481532+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.18810","created_at":"2026-07-05T10:08:52.481532+00:00"},{"alias_kind":"pith_short_12","alias_value":"AHG3TJA7WVGW","created_at":"2026-07-05T10:08:52.481532+00:00"},{"alias_kind":"pith_short_16","alias_value":"AHG3TJA7WVGWC47M","created_at":"2026-07-05T10:08:52.481532+00:00"},{"alias_kind":"pith_short_8","alias_value":"AHG3TJA7","created_at":"2026-07-05T10:08:52.481532+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2412.02640","citing_title":"On the optimality of coin-betting for mean estimation","ref_index":9,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AHG3TJA7WVGWC47M2UU2NMGDLS","json":"https://pith.science/pith/AHG3TJA7WVGWC47M2UU2NMGDLS.json","graph_json":"https://pith.science/api/pith-number/AHG3TJA7WVGWC47M2UU2NMGDLS/graph.json","events_json":"https://pith.science/api/pith-number/AHG3TJA7WVGWC47M2UU2NMGDLS/events.json","paper":"https://pith.science/paper/AHG3TJA7"},"agent_actions":{"view_html":"https://pith.science/pith/AHG3TJA7WVGWC47M2UU2NMGDLS","download_json":"https://pith.science/pith/AHG3TJA7WVGWC47M2UU2NMGDLS.json","view_paper":"https://pith.science/paper/AHG3TJA7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.18810&json=true","fetch_graph":"https://pith.science/api/pith-number/AHG3TJA7WVGWC47M2UU2NMGDLS/graph.json","fetch_events":"https://pith.science/api/pith-number/AHG3TJA7WVGWC47M2UU2NMGDLS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AHG3TJA7WVGWC47M2UU2NMGDLS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AHG3TJA7WVGWC47M2UU2NMGDLS/action/storage_attestation","attest_author":"https://pith.science/pith/AHG3TJA7WVGWC47M2UU2NMGDLS/action/author_attestation","sign_citation":"https://pith.science/pith/AHG3TJA7WVGWC47M2UU2NMGDLS/action/citation_signature","submit_replication":"https://pith.science/pith/AHG3TJA7WVGWC47M2UU2NMGDLS/action/replication_record"}},"created_at":"2026-07-05T10:08:52.481532+00:00","updated_at":"2026-07-05T10:08:52.481532+00:00"}